Timeline for What is the Plancherel Measure for $\textrm{SL}_3(\mathbb{Q}_p)$?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2012 at 5:45 | comment | added | anādimadhyānta | Aubert and Plymen have Plancherel formulas for GL(n, F) where F is p-adic : arxiv.org/abs/math/0302169 | |
| Nov 6, 2012 at 15:35 | comment | added | Marc Palm | What is a $SL_3(\mathbb{Z})$-automorphic Hecke eigenfunction? You do not mean a $SL_3(\mathbb{Z}_p)$-biinvariant function, because then everything is fairly easy and I can give the answer. | |
| Nov 6, 2012 at 15:25 | comment | added | anstei | I'm studying the local parameters of $\textrm{SL}_3(\mathbb{Z})$-automorphic Hecke eigenfunctions. We already have a measure $\mu_T$ satisfying $lim_{T \to \infty} \int_{\textrm{SL}_3(\mathbb{Q}_p)-\textrm{spectrum}} \chi_\rho(\pi) d \mu_T(\pi) = \alpha_p(\rho)$ and I'm looking for the limiting measure $\lim_{T \to \infty} \mu_T$. A natural candidate is the Plancherel measure. | |
| Nov 6, 2012 at 13:10 | comment | added | Marc Palm | In short, even Paul Garrett has no reference for the Plancherel of GL(n), which is easier than SL(n). | |
| Nov 6, 2012 at 13:06 | comment | added | Marc Palm | Also see Paul Garrett's answer here: mathoverflow.net/questions/70801/… | |
| Nov 6, 2012 at 13:05 | comment | added | Marc Palm | What do you need it for? Are you interested in it for its own sake? Do you know the Plancherel measure for $SL(2)$ or $GL(2)$? A wild guess is that beautiful formulas are only available for Hecke algebras associated to distinguished strata and that in principle there is an algorithm because the characters and representations of SL(N) have been classified. | |
| Nov 6, 2012 at 7:14 | answer | added | Paul Broussous | timeline score: 2 | |
| Nov 5, 2012 at 14:59 | history | asked | anstei | CC BY-SA 3.0 |